In some completions, annular barriers are often used for providing zone isolation, i.e. isolation of production zones from non-producing zones. The annular barriers are mounted as part of the well tubular structure, and an expandable sleeve of the annular barrier is arranged around the well tubular structure and is expanded to provide the zone isolation. In some wells, the annular space surrounding the annular barrier is so limited that the expandable sleeve cannot be mounted by means of connection sleeve parts surrounding the expandable sleeve to fasten the expandable sleeve to the base pipe. A mere welding of the ends of the expandable sleeve to the base pipe does not suffice, since tests have shown that there is a risk that the expandable sleeve will rupture or depart from the base pipe. This is due to the fact that the connection sleeve parts prevent free expansion of the expandable sleeve and thus limit the risk of the expandable sleeve rupturing during expansion.